arXiv subjects

Bertrand I. Halperin

Publications and source records attributed to Bertrand I. Halperin.

At least 91 records · Page 5Linked to original sources

arXiv2007

Particle-hole symmetry and the Pfaffian state

We consider the properties of the Moore-Read Pfaffian state under particle-hole conjugation. We show that the particle-hole conjugate of the Pfaffian state - or "anti-Pfaffian" state - is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished by both their bulk and edge physics though the difference is most dramatic at the edge: the edge of the anti-Pfaffian state has a composite structure that leads to a different thermal Hall conductance and different tunneling exponents than the Pfaffian state. At the same time, the two states are exactly degenerate in energy for a $ν= 5/2$ quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed $ν= 5/2$ quantum Hall plateau.

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arXiv2007

Theory of Spin Hall Effects in Semiconductors

Spin Hall effects are a collection of phenomena, resulting from spin-orbit coupling, in which an electrical current flowing through a sample can lead to spin transport in a perpendicular direction and spin accumulation at lateral boundaries. These effects, which do not require an applied magnetic field, can originate in a variety of intrinsic and extrinsic spin-orbit coupling mechanisms and depend on geometry, dimension, impurity scattering, and carrier density of the system--making the analysis of these effects a diverse field of research. In this article, we give an overview of the theoretical background of the spin Hall effects and summarize some of the most important results. First, we explain effective spin-orbit Hamiltonians, how they arise from band structure, and how they can be understood from symmetry considerations; including intrinsic coupling due to bulk inversion or structure asymmetry or due to strain, and extrinsic coupling due to impurities. This leads to different mechanisms of spin transport: spin precession, skew scattering, and side jump. Then we present the kinetic (Boltzmann) equations, which describe the spin-dependent distribution function of charge carriers, and the diffusion equation for spin polarization density. Next, we define the notion of spin currents and discuss their relation to spin polarization. Finally, we explain the electrically induced spin effects; namely, spin polarization and currents in bulk and near boundaries (the focus of most current theoretical research efforts), and spin injection, as well as effects in mesoscopic systems and in edge states.

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arXiv2007

Spin generation away from boundaries by nonlinear transport

In several situations of interest, spin polarization may be generated far from the boundaries of a sample by nonlinear effects of an electric current, even when such a generation is forbidden by symmetry in the linear regime. We present an analytically solvable model where spin accumulation results from a combination of current gradients, nonlinearity, and cubic anisotropy. Further, we show that even with isotropic conductivity, nonlinear effects in a low symmetry geometry can generate spin polarization far away from boundaries. Finally, we find that drift from the boundaries results in spin polarization patterns that dominate in recent experiments on GaAs by Sih et al. [Phys. Rev. Lett. 97, 096605 (2006)].

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arXiv2007

Cubic Dresselhaus Spin-Orbit Coupling in 2D Electron Quantum Dots

We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., $\propto p^3$) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using these results, together with previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on conductance through an 8 um^2 quantum dot [D M Zumbuhl et al., Phys. Rev. B 72, 081305 (2005)] suggests that 1) the GaAs Dresselhaus coupling constant, $γ$, is approximately 9 eVA^3, significantly less than the commonly cited value of 27.5 eVA^3 and 2) the majority of the spin-flip component of spin-orbit coupling can come from the cubic Dresselhaus term.

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arXiv2007

Magnetoconductance oscillations in quasiballistic multimode nanowires

We calculate the conductance of quasi-one-dimensional nanowires with electronic states confined to a surface charge layer, in the presence of a uniform magnetic field. Two-terminal magnetoconductance (MC) between two leads deposited on the nanowire via tunnel barriers is dominated by density-of-states (DOS) singularities, when the leads are well apart. There is also a mesoscopic correction due to a higher-order coherent tunneling between the leads for small lead separation. The corresponding MC structure depends on the interference between electron propagation via different channels connecting the leads, which in the simplest case, for the magnetic field along the wire axis, can be crudely characterized by relative winding numbers of paths enclosing the magnetic flux. In general, the MC oscillations are aperiodic, due to the Zeeman splitting, field misalignment with the wire axis, and a finite extent of electron distribution across the wire cross section, and are affected by spin-orbit coupling. The quantum-interference MC traces contain a wealth of information about the electronic structure of multichannel wires, which would be complimentary to the DOS measurements. We propose a four-terminal configuration to enhance the relative contribution of the higher-order tunneling processes and apply our results to realistic InAs nanowires carrying several quantum channels in the surface charge-accumulation layer.

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arXiv2006

Detection of current-induced spins by ferromagnetic contacts

Detection of current-induced spin accumulation via ferromagnetic contacts is discussed. Onsager's relations forbid that in a two-probe configuration spins excited by currents in time-reversal symmetric systems can be detected by switching the magnetization of a ferromangetic detector contact. Nevertheless, current-induced spins can be transferred as a torque to a contact magnetization and affect the charge currents in many-terminal configurations. We demonstrate the general concepts by solving the microscopic transport equations for the diffuse Rashba system with magnetic contacts.

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arXiv2006

Nonlocal magnetization dynamics in ferromagnetic heterostructures

Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents: On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation processes. We review recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density--functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful to understand the physics and to engineer the characteristics of small devices such as magnetic random-access memory elements.

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arXiv2006

Out-of-plane spin polarization from in-plane electric and magnetic fields

We show that the joint effect of spin-orbit and magnetic fields leads to a spin polarization perpendicular to the plane of a two-dimensional electron system with Rashba spin-orbit coupling and in-plane parallel dc magnetic and electric fields, for angle-dependent impurity scattering or nonparabolic energy spectrum, while only in-plane polarization persists for simplified models. We derive Bloch equations, describing the main features of recent experiments, including the magnetic field dependence of static and dynamic responses.

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arXiv2005

Domain Patterns in the Microwave-Induced Zero-Resistance State

It has been proposed that the microwave-induced ``zero-resistance'' phenomenon, observed in a GaAs two-dimensional electron system at low temperatures in moderate magnetic fields, results from a state with multiple domains, in which a large local electric field $\bE(\br)$ is oriented in different directions. We explore here the questions of what may determine the domain arrangement in a given sample, what do the domains look like in representative cases, and what may be the consequences of domain-wall localization on the macroscopic dc conductance. We consider both effects of sample boundaries and effects of disorder, in a simple model, which has a constant Hall conductivity, and is characterized by a Lyapunov functional.

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arXiv2005

Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state

We propose several experiments to test the non-abelian nature of quasi-particles in the fractional quantum Hall state of ν=5/2. One set of experiments studies interference contribution to back-scattering of current, and is a simplified version of an experiment suggested recently. Another set looks at thermodynamic properties of a closed system. Both experiments are only weakly sensitive to disorder-induced distribution of localized quasi-particles.

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arXiv2005

Theory of Spin Hall conductivity in n-doped GaAs

We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew scattering and side jump contributions to the spin Hall conductance. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with recent experiments by Kato et al. [Science 306, 1910 (2004)].

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arXiv2005

Theory of momentum resolved tunneling into a short quantum wire

Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large $N$ using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.

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arXiv2005

Steady States of a Microwave Irradiated Quantum Hall Gas

We consider effects of a long-wavelength disorder potential on the Zero Conductance State (ZCS) of the microwave-irradiated 2D electron gas. Assuming a uniform Hall conductivity, we construct a Lyapunov functional and derive stability conditions on the domain structure of the photo-generated fields. We solve the resulting equations for a general one-dimensional and certain two-dimensional disorder potentials, and find non-zero conductances, photo-voltages, and circulating dissipative currents. In contrast, weak white noise disorder does not destroy the ZCS, but induces mesoscopic current fluctuations.

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arXiv2004

Mean-field magnetization relaxation in conducting ferromagnets

Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can be formally eliminated by going into the rotating frame of reference for the spin dynamics. The ferromagnetic damping in this case grows linearly with the spin-flip rate when the latter is smaller than the exchange field and is inversely proportional to the spin-flip rate in the opposite limit. These two regimes are analogous to the "spin-pumping" and the "breathing Fermi-surface" damping mechanisms, respectively. In diluted ferromagnetic semiconductors, the hole-mediated magnetization can be efficiently relaxed to the itinerant-carrier degrees of freedom due to the strong spin-orbit interaction in the valence bands.

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arXiv2004

Many-body dispersions in interacting ballistic quantum wires

We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. We measure excitation spectra that clearly deviate from the non-interacting spectrum, attesting to the importance of Coulomb interactions. Notable is an observed 30% enhancement of the velocity of the main excitation branch relative to non-interacting electrons with the same density. In short wires, finite size effects resulting from broken translational invariance are observed. Spin - charge separation is manifested through moire patterns, reflecting different spin and charge excitation velocities.

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arXiv2003

Signatures of spin-charge separation in double--quantum-wire tunneling

We present evidence for spin-charge separation in the tunneling spectrum of a system consisting of two quantum wires connected by a long narrow tunnel junction at the edge of a GaAs/AlGaAs bilayer heterostructure. Multiple excitation velocities are detected in the system by tracing out electron spectral peaks in the conductance dependence on the applied voltage, governing the energy of tunneled electrons, and the magnetic field, governing the momentum shift along the wires. The boundaries of the wires are important and lead to a characteristic interference pattern in measurements on short junctions. We show that the experimentally observed modulation of the conductance oscillation amplitude as a function of the voltage bias can also be accounted for by spin-charge separation of the elementary excitations in the interacting wires.

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arXiv2003

Dynamic ferromagnetic proximity effect in photoexcited semiconductors

The spin dynamics of photoexcited carriers in semiconductors in contact with a ferromagnet is treated theoretically and compared with time-dependent Faraday rotation experiments. The long time response of the system is found to be governed by the first tens of picoseconds in which the excited plasma interacts strongly with the intrinsic interface between semiconductor and ferromagnet in spite of the existence of a Schottky barrier in equilibrium.

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arXiv2003

Composite Fermions and the Fermion-Chern-Simons Theory

The concept of composite fermions, and the related Fermion-Chern-Simons theory, have been powerful tools for understanding quantum Hall systems with a partially full lowest Landau level. We shall review some of the successes of the Fermion-Chern-Simons theory, as well as some limitations and outstanding issues.

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